1. **Stating the problem:** We are given four diagrams (a, b, c, d) described as nets and asked to determine which are nets, identify the 3D objects they form, verify the answers, and explain the reasoning. 2. **Understanding nets:** A net is a 2D pattern that can be folded along edges to form a 3D solid without overlaps or gaps. 3. **Analyzing each diagram:** - a) Central rectangle with two triangles attached above and below on opposite sides and one triangle attached to the right side. - This net has 1 rectangle and 3 triangles. - Triangles attached on opposite sides suggest folding into a 3D shape with triangular faces meeting at edges. - This matches the net of a triangular prism (rectangle base with triangular ends). - b) Three stacked rectangles vertically with a triangle attached to the right side of the top rectangle and one triangle attached to the left side of the middle rectangle. - The presence of three rectangles stacked suggests a prism-like shape. - Triangles attached on sides indicate possible folding into a shape with triangular faces. - However, the arrangement is unusual for a standard prism net; likely not a valid net because the triangles are on different rectangles and may not fold properly. - c) Vertical rectangle in the center with four triangles attached to each side forming a diamond shape. - One rectangle with four triangles on all sides. - Folding the triangles up would form a square pyramid (rectangle base with four triangular faces). - d) Five squares arranged in an "L" shape: four squares forming a 2x2 block and one square attached below the bottom left square. - This is a classic net of a cube (6 square faces). - Since only 5 squares are described, this net is incomplete for a cube. - But if the description implies the missing square is the base or top, it could be a cube net. 4. **Verification:** - a) Triangular prism net: 2 triangular bases and 3 rectangular faces. The description has 1 rectangle and 3 triangles, so it is incomplete for a triangular prism net (should have 2 rectangles and 2 triangles or 3 rectangles and 2 triangles). So a) is not a complete net. - b) Not a valid net due to triangle placement. - c) Square pyramid net: 1 square base and 4 triangular faces. The description matches perfectly. - d) Cube net requires 6 squares; only 5 are described, so incomplete net. 5. **Final conclusion:** - Only c) is a valid net, forming a square pyramid. 6. **Explanation:** - Nets must have all faces of the 3D shape represented and arranged so they fold without overlap. - c) has 1 rectangle (square base) and 4 triangles (sides), matching a square pyramid. - Others lack the correct number or arrangement of faces. **Answer:** Only diagram c) is a net, forming a square pyramid. **Desmos field:** empty since no graph requested.